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Published byMitchell Sharp Modified over 8 years ago

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Stem and leaf diagrams Sometimes called ‘stem and leaves’ too

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They really are as simple as they seem

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Simply a way of showing the values of data

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Example…….. Here are the weights of some aardvarks (kg): 12, 28, 17, 17, 19, 23, 9, 7, 25, 34, 21 Stem and leaf might look like this: Weight of aardvarks 0 9, 7 12, 7, 7, 9, 28, 3, 5, 1 KEY 34 1 2 is 12kg STEMLEAF OR LEAVES Don’t need to write this usually

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Your ‘stem and leaf’ must have a… 1.Title 2.Key – so that other people can work out what your values are.

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An ordered ‘stem and leaf’…. Has the values in size order.

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So for our example before… Weight of aardvarks 0 9, 7 12, 7, 7, 9, 28, 3, 5, 1 KEY 34 1 2 is 12kg The ordered ‘stem and leaf’ would be: Weight of aardvarks 0 7, 9 12, 7, 7, 9, 21, 3, 5, 8 KEY 34 1 2 is 12kg What weight does the ‘5’ represent?

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Show the following data as a stem and leaf diagram I.Q. scores of Year 10 girls: 105, 98, 112, 94, 130, 121, 98, 104, 100, 108, 112, 104, 101, 97, 104 I.Q. scores of Year 10 girls 9 8, 4, 8, 7 10 5, 4, 0, 8, 4, 1, 4 11 2, 2 12 1 13 0 KEY 11 2 means 112

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Now ‘order it’ I.Q. scores of Year 10 girls (unordered) 9 8, 4, 8, 7 10 5, 4, 0, 8, 4, 1, 4 11 2, 2 12 1 13 0 KEY 11 2 means 112 I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112

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The ordered one can be used to find lots of information

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Mode…. I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112 Mode – most common In this case 104

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Range …. I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112 Highest value – lowest value In this case: Range = 130 – 94 = 36

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Median …. I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112 1.Put in size order (already done); 2.then find the middle value In this case we have 15 values so we want the median = 104 8 th value along

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Lower Quartile …. I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112 1.Put in size order (already done); 2.then find the value a quarter of the way up In this case we have 15 values so we want the Lower quartile = 98 4 th value along

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Upper Quartile …. I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112 1.Put in size order (already done); 2.then find the value three- quarters of the way up In this case we have 15 values so we want the Upper quartile = 112 12 th value along

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You now know enough to be able to draw a ‘box and whisker diagram’ Smallest value Largest value median Lower quartile upper quartile 90 100 110 120 130 I.Q. Score

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Now for the boys……..

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Show the following data as a stem and leaf diagram I.Q. scores of Year 10 boys: 103, 98, 112, 99, 108, 122, 98, 104, 100, 108, 112, 104, 101, 97, 104, 108, 99, 108, 102 I.Q. scores of Year 10 boys 9 8, 9, 8, 7, 9 10 3,8,4,0,8,4,1,4,8,8,2 11 2, 2 12 2 KEY 11 2 means 112

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Now ‘order it’ I.Q. scores of Year 10 boys (unordered) 9 8, 9, 8, 7, 9 10 3,8,4,0,8,4,1,4,8,8,2 11 2, 2 12 2 KEY 11 2 means 112 I.Q. scores of Year 10 boys (ordered) 9 7, 8, 8, 9, 9 10 0,1,2,3,4,4,4,8,8,8,8 11 2, 2 12 2 KEY 11 2 means 112

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Mode …… I.Q. scores of Year 10 boys 9 7, 8, 8, 9, 9 10 0,1,2,3,4,4,4,8,8,8,8 11 2, 2 12 2 KEY 11 2 means 112 Mode – most common In this case 108

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Range …… I.Q. scores of Year 10 boys 9 7, 8, 8, 9, 9 10 0,1,2,3,4,4,4,8,8,8,8 11 2, 2 12 2 KEY 11 2 means 112 Highest value – lowest value In this case: Range = 122 – 97 = 25

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Median …… I.Q. scores of Year 10 boys 9 7, 8, 8, 9, 9 10 0,1,2,3,4,4,4,8,8,8,8 11 2, 2 12 2 KEY 11 2 means 112 1.Put in size order (already done); 2.then find the middle value In this case we have 19 values so we want the median = 104 10 th value

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Lower Quartile …… I.Q. scores of Year 10 boys 9 7, 8, 8, 9, 9 10 0,1,2,3,4,4,4,8,8,8,8 11 2, 2 12 2 KEY 11 2 means 112 1.Put in size order (already done); 2.then find the value a quarter of the way up In this case we have 19 values so we want the Lower quartile = 99 5 th value

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Upper Quartile …… I.Q. scores of Year 10 boys 9 7, 8, 8, 9, 9 10 0,1,2,3,4,4,4,8,8,8,8 11 2, 2 12 2 KEY 11 2 means 112 1.Put in size order (already done); 2.then find the value three- quarters of the way up In this case we have 19 values so we want the Upper quartile = 108 15 th value

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Now draw a box and whisker diagram to compare the I.Q. of boys and girls you can draw this one on the same diagram as before.

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Here we go ….. 90 100 110 120 130 I.Q. Score GIRLS BOYS What can you say about boys and girls I.Q.s ?

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